带有非局部效应的耦合流体模型的局部经典解

doi:10.12066/j.issn.1007-2861.2586

上海大学学报(自然科学版) ›› 2026, Vol. 32 ›› Issue (4): 728-740.doi: 10.12066/j.issn.1007-2861.2586

• 力学与土木工程 • 上一篇

带有非局部效应的耦合流体模型的局部经典解

黄宝云, 佟丽宁

上海大学理学院, 上海 200444

收稿日期:2024-05-11 发布日期:2026-09-04
通讯作者: 佟丽宁(1981—),女,博士,研究方向为偏微分方程.E-mail:tongln@shu.edu.cn E-mail:tongln@shu.edu.cn
基金资助:
国家自然科学基金资助项目(11901379)

Local classical solutions of coupled fluid models with non-local effects

HUANG Baoyun, TONG Lining

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2024-05-11 Published:2026-09-04

摘要/Abstract

摘要： 研究了一类带有非局部效应的流体模型.这类模型由可压缩Euler方程和不可压缩Navier-Stokes方程耦合构成,其中非局部项的通信核具有分数阶Laplacian算子结构.将Euler方程组等效重构为具有对称结构的双曲系统,在克服非局部项带来的非线性性质后,应用能量估计的方法,建立了此类模型初值问题的局部适定性理论和正则性准则.

关键词: 非局部效应, 分数阶Laplacian算子, 一致先验估计, 局部适定性

Abstract: This paper studied a class of fluid models with non-local effects, which consisted of compressible Euler equations coupled with incompressible Navier-Stokes equations, where the communication kernel of the non-local terms had a fractional Laplacian operator structure. Euler equations were reconstructed into a hyperbolic system with symmetric structure. After overcoming the nonlinear properties of non-local terms, the local well-posedness theory and regularity criterion were established for the initial value problems of such models by using the method of energy estimation.

Key words: non-local effect, fractional Laplacian operators, uniform priori estimation, local well-posedness

中图分类号:

O175.29

黄宝云, 佟丽宁. 带有非局部效应的耦合流体模型的局部经典解[J]. 上海大学学报(自然科学版), 2026, 32(4): 728-740.

HUANG Baoyun, TONG Lining. Local classical solutions of coupled fluid models with non-local effects[J]. Journal of Shanghai University（Natural Science Edition）, 2026, 32(4): 728-740.

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带有非局部效应的耦合流体模型的局部经典解

Local classical solutions of coupled fluid models with non-local effects

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